Related papers: Tensor field tomography with attenuation and refra…
Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the…
Transport maps have become a popular mechanic to express complicated probability densities using sample propagation through an optimized push-forward. Beside their broad applicability and well-known success, transport maps suffer from…
Optical Deflectometric Tomography (ODT) provides an accurate characterization of transparent materials whose complex surfaces present a real challenge for manufacture and control. In ODT, the refractive index map (RIM) of a transparent…
We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the…
The inverse source problem arising in photoacoustic tomography and in several other coupled-physics modalities is frequently solved by iterative algorithms. Such algorithms are based on the minimization of a certain cost functional. In…
Small-angle scattering tensor tomography is a technique for studying anisotropic nanostructures of millimeter-sized samples in a volume-resolved manner. It requires the acquisition of data through repeated tomographic rotations about an…
Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for…
This paper is devoted to deal with some mathematical and numerical aspects of the radiative integral transfer equations. First, the properties of the raidative integral operators are analyzed. Based on these results, the existence and…
Diffusive cosmic-ray transport in nonuniform large-scale magnetic fields in the presence of boundaries is considered. Reflecting and absorbing boundary conditions are derived for a modified telegraph equation with a convective term.…
The one-dimensional transverse field Ising model is solved by continuous unitary transformations in the high-field limit. A high accuracy is reached due to the closure of the relevant algebra of operators which we call string operators. The…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
In this work, we perform Bayesian inference tasks for the chemical master equation in the tensor-train format. The tensor-train approximation has been proven to be very efficient in representing high dimensional data arising from the…
Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples…
We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known…
The effects of thermal diffuse scattering on the transmission and eventual diffraction of highly accelerated electrons are investigated with a method that incorporates the frozen phonon approximation to the exact numerical solution of the…
We present a registration method for model reduction of parametric partial differential equations with dominating advection effects and moving features. Registration refers to the use of a parameter-dependent mapping to make the set of…
Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…
Column chromatography is a laboratory and industrial technique used to separate different substances mixed in a solution. Mathematically, it can be modelled using non-linear partial differential equations whose main ingredients are the…
In this work, an inverse problem on the determination of multiple coefficients arising from the time-domain diffuse optical tomography with fluorescence (DOT-FDOT) is investigated. We simultaneously recover the distribution of background…
We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…